If that's all there's to it, you can still use debootstrap, compile a kernel, and point the root parameter to your shiny new install.
If the official i386 arch was built with instructions that your hardware doesn't support, tough cookies.
While theoretically possible, that would only happen on processors older than 30 years. Debian's i386 architecture still uses -march=i686 as its baseline compiler target, which is the venerable Pentium Pro: https://en.wikipedia.org/wiki/P6_(microarchitecture)
It was used in the OLPC XO-1. The Cisco ASA line of firewalls also used Geode processors at least at some point in its lifetime.